MATH SOLVE

4 months ago

Q:
# Jen and David owe $22,000 in loans for their two cars. The amount of the loan for Jen’s car is $2,000 less than twice the amount of the loan for David’s car. Call the amount that Jen owes j and the amount that David owes d.

Accepted Solution

A:

Answer:David: $8,000Jen: $14,000Step-by-step explanation:The amount that Jen owes = jThe amount that David owes = dJen and David owe $22,000 in loans for their two cars, then[tex]j + d = 22,000[/tex]The amount of the loan for Jen’s car is $2,000 less than twice the amount of the loan for David’s car, thentwice the amount of the loan for David’s car = 2d$2,000 less than twice the amount of the loan for David’s car = 2d - 2,000then[tex]j = 2d -2,000[/tex]Solve the system of two equations:[tex]\left\{\begin{array}{l}j+d=22,000\\j=2d-2,000\end{array}\right.[/tex]Substitute the second equation into the first:[tex]2d-2,000+d=22,000\\ \\3d=24,000\\ \\d=8,000\\ \\j=2\cdot 8,000-2,000=16,000-2,000=14,000[/tex]